Super Market Sales Analysis¶

Team Members:¶

Shashank Kulkarni - A20542907
Soham Mankar - A20543251

¶

Data Collection¶

In [1]:
# Import required Libraries
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import matplotlib as mpl
import plotly.express as px
import plotly.figure_factory as ff
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from scipy.stats import skew
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
from sklearn.metrics import silhouette_score, mean_absolute_error, mean_squared_error, r2_score
from yellowbrick.cluster import KElbowVisualizer
import xgboost as xgb
from xgboost import XGBRegressor
import lightgbm as lgb
from catboost import CatBoostRegressor
from sklearn.linear_model import LinearRegression
from sklearn.ensemble import RandomForestRegressor
from sklearn.tree import DecisionTreeRegressor
from sklearn.svm import SVR
from sklearn.linear_model import PoissonRegressor
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split, cross_val_score, KFold
import statsmodels.api as sm
import statsmodels.formula.api as smf

import warnings



# Styling
%matplotlib inline
from termcolor import colored, cprint
mpl.rcParams['axes.unicode_minus'] = False
plt.rcParams["font.family"] = "cursive"


warnings.filterwarnings('ignore')
In [2]:
#Read the Data in Csv file 
Store=pd.read_csv("Stores.csv")
Store.head()
Out[2]:
Store ID Store_Area Items_Available Daily_Customer_Count Store_Sales
0 1 1659 1961 530 66490
1 2 1461 1752 210 39820
2 3 1340 1609 720 54010
3 4 1451 1748 620 53730
4 5 1770 2111 450 46620
In [3]:
#Size of Dataframe
Store.shape
Out[3]:
(896, 5)
In [4]:
#Checking the info of Dataframe
Store.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 896 entries, 0 to 895
Data columns (total 5 columns):
 #   Column                Non-Null Count  Dtype
---  ------                --------------  -----
 0   Store ID              896 non-null    int64
 1   Store_Area            896 non-null    int64
 2   Items_Available       896 non-null    int64
 3   Daily_Customer_Count  896 non-null    int64
 4   Store_Sales           896 non-null    int64
dtypes: int64(5)
memory usage: 35.1 KB
In [5]:
#Checking the Missing values
Store.isnull().sum()
Out[5]:
Store ID                0
Store_Area              0
Items_Available         0
Daily_Customer_Count    0
Store_Sales             0
dtype: int64

There are no Missing values in dataset¶

In [6]:
#Checking For Duplicates
Store.duplicated().sum()
Out[6]:
0

There are no Duplicates in data¶

In [7]:
# Let us drop "Store ID" feature, because as it is index it can be neglected and dropped

Store = Store.iloc[:, 1:]
Store.head()
Out[7]:
Store_Area Items_Available Daily_Customer_Count Store_Sales
0 1659 1961 530 66490
1 1461 1752 210 39820
2 1340 1609 720 54010
3 1451 1748 620 53730
4 1770 2111 450 46620
In [8]:
Store.columns
Out[8]:
Index(['Store_Area', 'Items_Available', 'Daily_Customer_Count', 'Store_Sales'], dtype='object')
In [9]:
# Let's see top 5 stores with highest sales

highest_sales = pd.DataFrame(Store.nlargest(5, ['Store_Sales']))
highest_sales
Out[9]:
Store_Area Items_Available Daily_Customer_Count Store_Sales
649 1989 2414 860 116320
868 1775 2104 980 105150
432 1365 1638 680 102920
408 1303 1587 1310 102310
758 1486 1758 820 101820
In [10]:
# show the top 5 stores with lowest sales

lowest_sales = pd.DataFrame(Store.nsmallest(5, ['Store_Sales']))
lowest_sales
Out[10]:
Store_Area Items_Available Daily_Customer_Count Store_Sales
31 1250 1508 990 14920
852 1477 1790 880 16370
775 1537 1877 660 17670
593 1624 1946 870 20270
352 1397 1686 850 21300

Insights:¶

  • The store with the highest sales has an area of 1989 and 2414 items available, but there are stores with smaller areas and fewer items available that still make it into the top 5. This indicates that larger store size or inventory does not necessarily result in higher sales.
  • Sales figures for the top stores are concentrated above 100,000, with the top store making significantly more than the others at 116,320. This could suggest a standout location or strategy that enables higher performance.
  • Interestingly, the stores with the lowest sales have relatively high daily customer counts, in some cases higher than those in the top 5. This could indicate inefficiencies in sales conversion or possibly lower average transaction values.
  • The bottom stores sales figures are less varied than the top stores, ranging from 14,920 to 21,300. This may point to a consistent challenge faced by these stores in generating higher sales.

¶

Note: Our Target Variable is 'Store_Sales', which indicates Sales in US dollars that stores made¶

¶

Exploratory Data Analysis¶

In [11]:
#Describing the dataframe
Store.describe()
Out[11]:
Store_Area Items_Available Daily_Customer_Count Store_Sales
count 896.000000 896.000000 896.000000 896.000000
mean 1485.409598 1782.035714 786.350446 59351.305804
std 250.237011 299.872053 265.389281 17190.741895
min 775.000000 932.000000 10.000000 14920.000000
25% 1316.750000 1575.500000 600.000000 46530.000000
50% 1477.000000 1773.500000 780.000000 58605.000000
75% 1653.500000 1982.750000 970.000000 71872.500000
max 2229.000000 2667.000000 1560.000000 116320.000000

Observations:¶

- Maximum Store Area is 2229 and Minimum Store Area is 1485.409598.

- Highest Daily customer count is 1560 on an average over month.

- The minimum daily customer count is 10, which is very low compared to the maximum of 1560. This range suggests that
  some stores are underperforming or could be newly opened, while others are high-traffic.

- On a whole Maximum Store Sale is 116320 and MInimum Sale is 14920.

Now let's findout correlation between variables¶

In [12]:
#coorelation matrix

Store.corr()
Out[12]:
Store_Area Items_Available Daily_Customer_Count Store_Sales
Store_Area 1.000000 0.998891 -0.041423 0.097474
Items_Available 0.998891 1.000000 -0.040978 0.098849
Daily_Customer_Count -0.041423 -0.040978 1.000000 0.008629
Store_Sales 0.097474 0.098849 0.008629 1.000000
In [13]:
# Let's see the correlation between variables using heatmap

plt.figure(figsize = (8, 5))
sns.heatmap(Store.corr(), annot = True, cmap = 'rocket_r')
Out[13]:
<Axes: >

Insights from above HeatMap¶

  • Store Area and Items avaliable shows strong positive correlationship

  • Store area and Items available has a linear relationship

  • Store area and Items available has more impact on store sales rather than daily customers

  • The correlation coefficients are -0.041 for Store Area/Items Available and Daily Customer Count, which indicates a very weak negative correlation. This implies that the store area and the number of items available have almost no effect on the daily number of customers.

  • There is very Weak Positive Correlation Between Store Area/Items Available and Store Sales that is correlation coefficients are 0.097 and 0.099 respectively.

  • There is No Correlation Between Daily Customer Count and Store Sales that is the correlation coefficient is 0.0086, which is very close to zero.

Now Lets check if the Variables of dataset are normally distributed or not¶

In [14]:
fig, axs = plt.subplots(2, 2, figsize=(10,10))
fig.tight_layout(pad=4.0)

features = ['Store_Area', 'Items_Available', 'Daily_Customer_Count','Store_Sales']

for f,ax in zip(features,axs.ravel()):
    ax=sns.histplot(ax=ax,data=Store,x=Store[f],kde=True)
    ax.set_title('Feature:'+ f)
In [15]:
sns.set_theme(style="ticks",palette='deep')
sns.pairplot(Store)
Out[15]:
<seaborn.axisgrid.PairGrid at 0x24a92304f90>

Insights for above plots:¶

  • The variables Store_Area,Items_avaliable,Daily_customer_count and Store_Sales are "Normally Distributed", with the presence of outliers indicated by the bars at the tails of each histogram

  • In the above second plot, the scatter plot for Store Area vs. Items Available shows a clear positive linear relationship, with data points closely aligned along a line.

Now lets check for Skewness between all of them:¶

In [16]:
skew_df = pd.DataFrame(data= Store.columns, columns= ['Features'])
skew_df['Skew'] = skew_df['Features'].apply(lambda feature: skew(Store[feature]))
skew_df['Abs Skew'] = skew_df['Skew'].apply(abs)
skew_df['Skewed'] = skew_df['Abs Skew'].apply(lambda x: True if x > 0.5 else False)
skew_df
Out[16]:
Features Skew Abs Skew Skewed
0 Store_Area 0.030316 0.030316 False
1 Items_Available 0.034382 0.034382 False
2 Daily_Customer_Count 0.074508 0.074508 False
3 Store_Sales 0.148544 0.148544 False

None of the features or the target variable (assuming one of these is the target for your analysis) show significant skewness. Since all skewness values are well below the threshold of 0.5, this suggests that the data distributions are approximately symmetrical, resembling a normal distribution.Therefore we don't need to apply any kind of transformation¶

¶

Now Lets Do some Bi-Variate Analysis¶

Let's examine the relationships between our variables by creating a scatter plot.¶

In [17]:
# Create a figure with 4 subplots (2x2)
fig, axes = plt.subplots(2, 2, figsize=(14, 10))

# Flatten the axes array for easy indexing
axes = axes.flatten()

# Scatterplot for Store_Sales vs. Store_Area
sns.scatterplot(ax=axes[0], data=Store, x='Store_Sales', y='Store_Area')
axes[0].set_title('Store Sales vs Store Area')

# Scatterplot for Store_Sales vs. Items_Available
sns.scatterplot(ax=axes[1], data=Store, x='Store_Sales', y='Items_Available')
axes[1].set_title('Store Sales vs Items Available')

# Scatterplot for Store_Area vs. Daily_Customer_Count
sns.scatterplot(ax=axes[2], data=Store, x='Store_Area', y='Daily_Customer_Count')
axes[2].set_title('Store Area vs Daily Customer Count')

# Scatterplot for Items_Available vs. Daily_Customer_Count
sns.scatterplot(ax=axes[3], data=Store, x='Items_Available', y='Daily_Customer_Count')
axes[3].set_title('Items Available vs Daily Customer Count')

# Adjust the layout
plt.tight_layout()

# Show the plots
plt.show()

From the scatter plots, we observe no clear patterns, as the values are mostly clustered around their mean and not easily interpretable. Thus, we will opt for a contour plot for a more detailed analysis.¶

In [18]:
res = sns.kdeplot(x=Store['Store_Sales'], y=Store['Store_Area'], shade=True, cmap="Reds_r")
plt.show()

res = sns.kdeplot(x= Store['Store_Sales'], y= Store['Items_Available'], shade = True, cmap = "Reds_r")
plt.show()

res = sns.kdeplot(x= Store['Store_Sales'], y= Store['Daily_Customer_Count'], shade = True, cmap = "Reds_r")
plt.show()

From the three plots related to daily sales, we can deduce that stores with daily sales ranging from 40K to 80K typically share these characteristics:¶

  • The size of the store is usually between 1,250 and 1,750 square feet.
  • The number of items available falls within the range of 1,600 to 2,000.
  • The daily number of customers is generally between 520 and 1,000.
In [19]:
res = sns.kdeplot(x= Store['Daily_Customer_Count'], y=Store['Store_Area'], shade = True, cmap = "Greens_r")
plt.show()
res = sns.kdeplot(x= Store['Daily_Customer_Count'], y=Store['Items_Available'], shade = True, cmap = "Greens_r")
plt.show()

From above 2 plots against daily_sales¶

Stores having daily cusotmers between 510 to 1000 have the following aspects:

  • The store size should be between 1250 to 1750.

  • The number of items availble should be between 1500 to 2000

¶

Now lets findout the outliers in the data and if there are any we will remove them¶

In [20]:
#lets findout if there are any outliers

sns.set_context('poster', font_scale= 0.6)
fig, ax  = plt.subplots(2, 2, figsize= (20, 10))

plt.suptitle('Boxplot of all Numerical columns', fontsize = 20)

ax1 = sns.boxplot(x = Store['Store_Area'], color= '#4fcf31', ax= ax[0, 0])
ax1.set(xlabel= 'Store Area')

ax2 = sns.boxplot(x = Store['Items_Available'], color= '#4fcf31', ax= ax[0, 1])
ax2.set(xlabel= 'Items Available')

ax3 = sns.boxplot(x = Store['Daily_Customer_Count'], color= '#4fcf31', ax= ax[1, 0])
ax3.set(xlabel= 'Daily Customer Count')

ax4 = sns.boxplot(x = Store['Store_Sales'], color= '#4fcf31', ax= ax[1, 1])
ax4.set(xlabel= 'Store Sales')

plt.show()
In [21]:
# Function to remove outliers for a specific column
def remove_outliers(df, column):
    Q1 = df[column].quantile(0.25)
    Q3 = df[column].quantile(0.75)
    IQR = Q3 - Q1
    lower_bound = Q1 - 1.5 * IQR
    upper_bound = Q3 + 1.5 * IQR
    # Return the DataFrame without outliers
    return df[(df[column] >= lower_bound) & (df[column] <= upper_bound)]

# Assume 'Store' is your DataFrame and has been defined with the appropriate data
# Plot boxplots for all columns to visualize outliers
plt.figure(figsize=(12, 8))
for i, column in enumerate(Store.columns, 1):
    plt.subplot(2, 2, i)
    sns.boxplot(data=Store, y=column)
    plt.title(f'Boxplot of {column}')
plt.tight_layout()
plt.show()

# Remove outliers for each column in the DataFrame
for column in Store.columns:
    Store = remove_outliers(Store, column)

# Reset index after removing outliers
Store.reset_index(drop=True, inplace=True)

# Display the first few rows of the DataFrame with outliers removed
print(Store.head())

   Store_Area  Items_Available  Daily_Customer_Count  Store_Sales
0        1659             1961                   530        66490
1        1461             1752                   210        39820
2        1340             1609                   720        54010
3        1451             1748                   620        53730
4        1770             2111                   450        46620

¶

In [22]:
from sklearn.decomposition import PCA
from sklearn.manifold import TSNE
import umap.umap_ as umap



# Standardizing the data
scaler = StandardScaler()
store_scaled = scaler.fit_transform(Store)

# PCA
pca = PCA(n_components=2)
pca_result = pca.fit_transform(store_scaled)

# t-SNE
tsne = TSNE(n_components=2, perplexity=30, n_iter=300)
tsne_result = tsne.fit_transform(store_scaled)

# UMAP
umap_model = umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2)
umap_result = umap_model.fit_transform(store_scaled)

# Plotting results
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# PCA plot
axs[0].scatter(pca_result[:,0], pca_result[:,1])
axs[0].set_title('PCA Result')
axs[0].set_xlabel('Principal Component 1')
axs[0].set_ylabel('Principal Component 2')

# t-SNE plot
axs[1].scatter(tsne_result[:,0], tsne_result[:,1])
axs[1].set_title('t-SNE Result')
axs[1].set_xlabel('t-SNE Feature 1')
axs[1].set_ylabel('t-SNE Feature 2')

# UMAP plot
axs[2].scatter(umap_result[:,0], umap_result[:,1])
axs[2].set_title('UMAP Result')
axs[2].set_xlabel('UMAP Feature 1')
axs[2].set_ylabel('UMAP Feature 2')

plt.tight_layout()
plt.show()

Insights:¶

  • PCA (Principal Component Analysis) Result: The PCA plot shows the data projected onto the first two principal components. PCA is a linear dimensionality reduction technique that identifies the axes (principal components) that maximize the variance in the data. The scatter plot is quite dense in the center, suggesting that the variance along these two principal components is relatively spread out, but with no clear separation or clusters of data points.
  • t-SNE (t-Distributed Stochastic Neighbor Embedding) Result: The t-SNE plot is much more spread out than the PCA plot, with the data points forming several distinct clusters. t-SNE is a non-linear technique particularly well-suited for visualizing high-dimensional data in two or three dimensions. The separation and formation of clusters suggest that t-SNE is able to capture the local structures and relationships between data points more effectively than PCA for this dataset.
  • UMAP (Uniform Manifold Approximation and Projection) Result: The UMAP plot also shows clusters, similar to t-SNE, but with a different structure. UMAP is another non-linear dimensionality reduction technique that is generally faster than t-SNE and often preserves more of the global structure. The clusters in the UMAP plot appear less dense than in the t-SNE plot, indicating that UMAP might be emphasizing both local and global structures of the data.

¶

¶

Data preprocessing¶

Choosing the Appropriate Features and then splitting into train-test split¶

In [23]:
feature_cols = ['Store_Area', 'Items_Available', 'Daily_Customer_Count']
X = Store[feature_cols]
y = Store['Store_Sales']
In [24]:
print(X.head())

   Store_Area  Items_Available  Daily_Customer_Count
0        1659             1961                   530
1        1461             1752                   210
2        1340             1609                   720
3        1451             1748                   620
4        1770             2111                   450
In [25]:
print(y.head())

0    66490
1    39820
2    54010
3    53730
4    46620
Name: Store_Sales, dtype: int64
In [26]:
#Splitting into train test

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.20, random_state = 42)
In [27]:
print(X_test.shape)
print(y_test.shape)

(178, 3)
(178,)
In [28]:
print(X_train.shape)
print(y_train.shape)

(709, 3)
(709,)
Note: the above data is for final data after removing outliers¶
In [29]:
# Standardizing our data for model improvement
sc = StandardScaler()
X = sc.fit_transform(X)

¶

Data Modeling¶

Data Modeling before Clustering¶

In [30]:
rfr = RandomForestRegressor(bootstrap = True, max_depth = 90, max_features = 2, min_samples_leaf = 4, min_samples_split = 12, n_estimators = 100)
rfr.fit(X_train, y_train)
r_pred = rfr.predict(X_test)
In [31]:
mse = mean_squared_error(y_test, r_pred)
rmse = np.sqrt(mean_squared_error(y_test, r_pred))
mae = mean_absolute_error(y_test, r_pred)

score = rfr.score(X_train, y_train) 
scores = cross_val_score(rfr, X_train, y_train,cv=10)
kfold = KFold(n_splits=10, shuffle=True)
kf_cv_scores = cross_val_score(rfr, X_train, y_train, cv=kfold )
In [32]:
print('RandomForest Regressor')
print("MSE: %.2f" % mse)
print("RMSE: %.2f" % (rmse))
print("MAE: %.2f" % (mae))
print("Training score: ", score)
print("Mean cross-validation score: %.2f" % scores.mean())
print("K-fold CV average score: %.2f" % kf_cv_scores.mean())

RandomForest Regressor
MSE: 369599567.55
RMSE: 19224.97
MAE: 15891.44
Training score:  0.40267339534749447
Mean cross-validation score: -0.07
K-fold CV average score: -0.07
In [33]:
plt.figure(figsize = (15, 6))
x_ax = range(len(y_test))
plt.plot(x_ax, y_test, label="original")
plt.plot(x_ax, r_pred, label="predicted")
plt.title("Sales test and predicted data")
plt.legend()
plt.show()

Data mining¶

We will find the ratio of Store Area , Items and Customers to know the purchasing power of a particular store For that we will make a copy of the original dataset¶

In [34]:
sales_data_avgs = Store.copy()
sales_data_avgs.head()
Out[34]:
Store_Area Items_Available Daily_Customer_Count Store_Sales
0 1659 1961 530 66490
1 1461 1752 210 39820
2 1340 1609 720 54010
3 1451 1748 620 53730
4 1770 2111 450 46620
In [35]:
sales_data_avgs['ratio_items/cutomers'] = sales_data_avgs['Items_Available']/sales_data_avgs['Daily_Customer_Count']
sales_data_avgs['ratio_size/customers'] = sales_data_avgs['Store_Area']/sales_data_avgs['Daily_Customer_Count']
sales_data_avgs['ratio_size/items']     = sales_data_avgs['Store_Area']/sales_data_avgs['Items_Available']
sales_data_avgs['target_sales'] = Store['Store_Sales']
In [36]:
sales_data_avgs.drop(['Store_Area','Items_Available','Daily_Customer_Count','Store_Sales'],axis = 1, inplace = True)
sales_data_avgs.head()
Out[36]:
ratio_items/cutomers ratio_size/customers ratio_size/items target_sales
0 3.700000 3.130189 0.845997 66490
1 8.342857 6.957143 0.833904 39820
2 2.234722 1.861111 0.832815 54010
3 2.819355 2.340323 0.830092 53730
4 4.691111 3.933333 0.838465 46620
In [37]:
sns.pairplot(data = sales_data_avgs)
Out[37]:
<seaborn.axisgrid.PairGrid at 0x24a9b7cc350>
In [38]:
x= sales_data_avgs.drop('target_sales',axis= 1)
clusters = []

for i in range(1, 15):
    km = KMeans(n_clusters=i).fit(x)
    clusters.append(km.inertia_)
    
sns.lineplot(x=list(range(1, 15)), y=clusters)
plt.xlabel('Clusters')
plt.ylabel('Inertia')
Out[38]:
Text(0, 0.5, 'Inertia')

The graph above indicates that the data can be categorized into 10 distinct segments for classifying the purchasing power of customers.¶

In [39]:
km_10 = KMeans(n_clusters=10).fit(X)
x['Labels'] =km_10.labels_
x.head()
Out[39]:
ratio_items/cutomers ratio_size/customers ratio_size/items Labels
0 3.700000 3.130189 0.845997 1
1 8.342857 6.957143 0.833904 1
2 2.234722 1.861111 0.832815 0
3 2.819355 2.340323 0.830092 1
4 4.691111 3.933333 0.838465 4
In [40]:
y = sales_data_avgs['target_sales']

Creating group for target sales based on labels¶

In [41]:
sales_join = x.join(y)
sales_join.columns
Out[41]:
Index(['ratio_items/cutomers', 'ratio_size/customers', 'ratio_size/items',
       'Labels', 'target_sales'],
      dtype='object')
In [42]:
sales_x = sales_join[['Labels','target_sales']]

x1= sales_x
clusters = []

for i in range(1, 15):
    km = KMeans(n_clusters=i).fit(x1)
    clusters.append(km.inertia_)
    
sns.lineplot(x=list(range(1, 15)), y=clusters)
plt.xlabel('Clusters')
plt.ylabel('Inertia')
Out[42]:
Text(0, 0.5, 'Inertia')
In [43]:
km_10 = KMeans(n_clusters=10).fit(x1)
x['Target_Groups'] =km_10.labels_
x.head()
Out[43]:
ratio_items/cutomers ratio_size/customers ratio_size/items Labels Target_Groups
0 3.700000 3.130189 0.845997 1 8
1 8.342857 6.957143 0.833904 1 0
2 2.234722 1.861111 0.832815 0 2
3 2.819355 2.340323 0.830092 1 2
4 4.691111 3.933333 0.838465 4 5

Data Modeling after clustering¶

Used 6 models with 10 FOLD cross validation for model comparison:¶

  • LinearRegression
  • DecisionTreeRegressor
  • XGBRegressor
  • LGBMRegressor
  • CatBoostRegressor
  • RandomForestRegressor

Used StandardScaler() for scaling.

Evaluation metrics: mae, mse, rmse, R2_score

In [44]:
#X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.20, random_state = 42) 
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size = 0.20, random_state = 42)

Linear Regression¶

In [45]:
lr = LinearRegression()
lr.fit(X_train, y_train)
lr_pred =lr.predict(X_test)
In [46]:
mse = mean_squared_error(y_test, lr_pred)
rmse = np.sqrt(mean_squared_error(y_test, lr_pred))
mae = mean_absolute_error(y_test, lr_pred)

score = lr.score(X_train, y_train) 
scores = cross_val_score(lr, X_train, y_train,cv=10)
kfold = KFold(n_splits=10, shuffle=True)
kf_cv_scores = cross_val_score(lr, X_train, y_train, cv=kfold )
r2 =r2_score(y_test,  lr_pred)
In [47]:
print('Linear Regression')
print("MSE: %.2f" % mse)
print("RMSE: %.2f" % (rmse))
print("MAE: %.2f" % (mae))
print("Training score: ", score)
print("Mean cross-validation score: %.2f" % scores.mean())
print("K-fold CV average score: %.2f" % kf_cv_scores.mean())
print("R_score : %.2f"%(r2))

Linear Regression
MSE: 287937214.68
RMSE: 16968.71
MAE: 12963.89
Training score:  0.16076622904615534
Mean cross-validation score: 0.14
K-fold CV average score: 0.14
R_score : 0.10
In [48]:
plt.figure(figsize = (15, 6))
x_ax = range(len(y_test))
plt.plot(x_ax, y_test, label="original")
plt.plot(x_ax, lr_pred, label="predicted")
plt.title("Sales test and predicted data")
plt.legend()
plt.show()

Decision Tree Regressor¶

In [49]:
dtr = DecisionTreeRegressor()
dtr.fit(X_train, y_train)
dtr_pred =dtr.predict(X_test)
In [50]:
mse = mean_squared_error(y_test, dtr_pred)
rmse = np.sqrt(mean_squared_error(y_test, dtr_pred))
mae = mean_absolute_error(y_test, dtr_pred)

score = dtr.score(X_train, y_train) 
scores = cross_val_score(dtr, X_train, y_train,cv=10)
kfold = KFold(n_splits=10, shuffle=True)
kf_cv_scores = cross_val_score(dtr, X_train, y_train, cv=kfold )
r2 =r2_score(y_test,  dtr_pred)
In [51]:
print('DecisionTree Regressor')
print("MSE: %.2f" % mse)
print("RMSE: %.2f" % (rmse))
print("MAE: %.2f" % (mae))
print("Training score: ", score)
print("Mean cross-validation score: %.2f" % scores.mean())
print("K-fold CV average score: %.2f" % kf_cv_scores.mean())
print("R_score : %.2f"%(r2))

DecisionTree Regressor
MSE: 12182677.53
RMSE: 3490.37
MAE: 2708.31
Training score:  1.0
Mean cross-validation score: 0.97
K-fold CV average score: 0.97
R_score : 0.96
In [52]:
plt.figure(figsize = (15, 6))
x_ax = range(len(y_test))
plt.plot(x_ax, y_test, label="original")
plt.plot(x_ax, dtr_pred, label="predicted")
plt.title("Sales test and predicted data")
plt.legend()
plt.show()

XGB Regressor¶

In [53]:
xgbr = XGBRegressor(random_state = 116)
xgbr.fit(X_train, y_train)
xgbr_pred =xgbr.predict(X_test)
In [54]:
mse = mean_squared_error(y_test, xgbr_pred)
rmse = np.sqrt(mean_squared_error(y_test, xgbr_pred))
mae = mean_absolute_error(y_test, xgbr_pred)

score = xgbr.score(X_train, y_train) 
scores = cross_val_score(xgbr, X_train, y_train,cv=10)
kfold = KFold(n_splits=10, shuffle=True)
kf_cv_scores = cross_val_score(xgbr, X_train, y_train, cv=kfold )
r2 =r2_score(y_test,  xgbr_pred)
In [55]:
print('XGB Regressor')
print("MSE: %.2f" % mse)
print("RMSE: %.2f" % (rmse))
print("MAE: %.2f" % (mae))
print("Training score: ", score)
print("Mean cross-validation score: %.2f" % scores.mean())
print("K-fold CV average score: %.2f" % kf_cv_scores.mean())
print("R_score : %.2f"%(r2))

XGB Regressor
MSE: 8817106.20
RMSE: 2969.36
MAE: 2312.64
Training score:  0.9997722585951683
Mean cross-validation score: 0.98
K-fold CV average score: 0.98
R_score : 0.97
In [56]:
plt.figure(figsize = (15, 6))
x_ax = range(len(y_test))
plt.plot(x_ax, y_test, label="original")
plt.plot(x_ax, xgbr_pred, label="predicted")
plt.title("Sales test and predicted data")
plt.legend()
plt.show()

LGBM Regressor¶

In [57]:
lgbr = lgb.LGBMRegressor(random_state = 116)
lgbr.fit(X_train, y_train)
lgbr_pred =lgbr.predict(X_test)

[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000405 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 731
[LightGBM] [Info] Number of data points in the train set: 709, number of used features: 5
[LightGBM] [Info] Start training from score 58643.004231
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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In [58]:
mse = mean_squared_error(y_test, lgbr_pred)
rmse = np.sqrt(mean_squared_error(y_test, lgbr_pred))
mae = mean_absolute_error(y_test, lgbr_pred)

score = lgbr.score(X_train, y_train) 
scores = cross_val_score(lgbr, X_train, y_train,cv=10)
kfold = KFold(n_splits=10, shuffle=True)
kf_cv_scores = cross_val_score(lgbr, X_train, y_train, cv=kfold )
r2 =r2_score(y_test,  lgbr_pred)

[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000654 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58521.598746
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000273 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58805.047022
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000324 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58671.677116
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000212 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58642.319749
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000331 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58956.018809
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000320 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58583.072100
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000310 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58640.266458
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000272 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58801.927900
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000165 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58593.228840
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000269 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 662
[LightGBM] [Info] Number of data points in the train set: 639, number of used features: 5
[LightGBM] [Info] Start training from score 58215.555556
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000258 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58387.633229
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000302 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58389.984326
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000287 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58420.752351
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000399 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 59121.003135
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000298 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 59015.203762
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000402 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58404.420063
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000762 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58132.366771
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000322 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 58362.100313
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000345 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 659
[LightGBM] [Info] Number of data points in the train set: 638, number of used features: 5
[LightGBM] [Info] Start training from score 59349.608150
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000260 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 662
[LightGBM] [Info] Number of data points in the train set: 639, number of used features: 5
[LightGBM] [Info] Start training from score 58846.651017
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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In [59]:
print('LGBM Regressor')
print("MSE: %.2f" % mse)
print("RMSE: %.2f" % (rmse))
print("MAE: %.2f" % (mae))
print("Training score: ", score)
print("Mean cross-validation score: %.2f" % scores.mean())
print("K-fold CV average score: %.2f" % kf_cv_scores.mean())
print("R_score : %.2f"%(r2))

LGBM Regressor
MSE: 16754909.80
RMSE: 4093.28
MAE: 2900.06
Training score:  0.9875222305276621
Mean cross-validation score: 0.93
K-fold CV average score: 0.92
R_score : 0.95
In [60]:
plt.figure(figsize = (15, 6))
x_ax = range(len(y_test))
plt.plot(x_ax, y_test, label="original")
plt.plot(x_ax, lgbr_pred, label="predicted")
plt.title("Sales test and predicted data")
plt.legend()
plt.show()

CatBoost Regressor¶

In [61]:
cbr = CatBoostRegressor(random_state =116, verbose = 0)
cbr.fit(X_train, y_train)
cbr_pred =cbr.predict(X_test)
In [62]:
mse = mean_squared_error(y_test, cbr_pred)
rmse = np.sqrt(mean_squared_error(y_test, cbr_pred))
mae = mean_absolute_error(y_test, cbr_pred)

score = cbr.score(X_train, y_train) 
scores = cross_val_score(cbr, X_train, y_train,cv=10)
kfold = KFold(n_splits=10, shuffle=True)
kf_cv_scores = cross_val_score(cbr, X_train, y_train, cv=kfold )
r2 =r2_score(y_test,  cbr_pred)
In [63]:
print('CatBoost Regressor')
print("MSE: %.2f" % mse)
print("RMSE: %.2f" % (rmse))
print("MAE: %.2f" % (mae))
print("Training score: ", score)
print("Mean cross-validation score: %.2f" % scores.mean())
print("K-fold CV average score: %.2f" % kf_cv_scores.mean())
print("R_score : %.2f"%(r2))

CatBoost Regressor
MSE: 8415036.42
RMSE: 2900.87
MAE: 2260.09
Training score:  0.9949993348317842
Mean cross-validation score: 0.98
K-fold CV average score: 0.98
R_score : 0.97
In [64]:
plt.figure(figsize = (15, 6))
x_ax = range(len(y_test))
plt.plot(x_ax, y_test, label="original")
plt.plot(x_ax, cbr_pred, label="predicted")
plt.title("Sales test and predicted data")
plt.legend()
plt.show()

Random Forest Regressor¶

In [65]:
rf = RandomForestRegressor(random_state = 116)
rf.fit(X_train, y_train)
rf_pred =rf.predict(X_test)
In [66]:
mse = mean_squared_error(y_test, rf_pred)
rmse = np.sqrt(mean_squared_error(y_test, rf_pred))
mae = mean_absolute_error(y_test, rf_pred)

score = rf.score(X_train, y_train) 
scores = cross_val_score(rf, X_train, y_train,cv=10)
kfold = KFold(n_splits=10, shuffle=True)
kf_cv_scores = cross_val_score(rf, X_train, y_train, cv=kfold )
r2 =r2_score(y_test,  rf_pred)
In [67]:
print('Random Forest Regressor')
print("MSE: %.2f" % mse)
print("RMSE: %.2f" % (rmse))
print("MAE: %.2f" % (mae))
print("Training score: ", score)
print("Mean cross-validation score: %.2f" % scores.mean())
print("K-fold CV average score: %.2f" % kf_cv_scores.mean())
print("R_score : %.2f"%(r2))

Random Forest Regressor
MSE: 7874184.48
RMSE: 2806.10
MAE: 2221.10
Training score:  0.9971815560983069
Mean cross-validation score: 0.98
K-fold CV average score: 0.98
R_score : 0.98
In [68]:
plt.figure(figsize = (15, 6))
x_ax = range(len(y_test))
plt.plot(x_ax, y_test, label="original")
plt.plot(x_ax, rf_pred, label="predicted")
plt.title("Sales test and predicted data")
plt.legend()
plt.show()
In [69]:
# parameters
class PARAM:
    FOLD = 10
    RANDOM_STATE = 116
    VERBOSE = 0
    
# scaling function
def Scaler(train_X, val_X):
    scaler = StandardScaler()
    scaled_train = scaler.fit_transform(train_X)
    scaled_val = scaler.transform(val_X)
    return scaled_train, scaled_val

# define models
xgbr = XGBRegressor(random_state = PARAM.RANDOM_STATE)
lgbr = lgb.LGBMRegressor(random_state = PARAM.RANDOM_STATE)
cbr = CatBoostRegressor(random_state = PARAM.RANDOM_STATE, verbose = PARAM.VERBOSE)
rf = RandomForestRegressor(random_state = PARAM.RANDOM_STATE)
dtr = DecisionTreeRegressor()
lr = LinearRegression()

classifiers_name = ['XGBRegressor','LGBMRegressor','CatBoostRegressor','RandomForestRegressor','DecisionTreeRegressor','LinearRegression']
color_sequence = ['red','blue','green','grey','cyan','yellow']
classifiers = [xgbr, lgbr, cbr, rf, dtr, lr]
mae_score = []
mse_score = []
rmse_score = []
R2_score = []

fold = KFold(n_splits=PARAM.FOLD, shuffle=True, random_state=PARAM.FOLD)

# 10 fold
for idx, classifier in enumerate(classifiers):
    mae = 0  
    mse = 0
    rmse = 0
    r2score = 0
    print(colored('Classifier:',color_sequence[idx]) ,colored(classifiers_name[idx],color_sequence[idx]), '\n\n')
    for fold_idx, (train_idx, val_idx) in enumerate(fold.split(X, y)):
        
        x_train, x_val = x.iloc[train_idx], x.iloc[val_idx]
        x_train, x_val = Scaler(x_train, x_val)
        y_train, y_val = y.iloc[train_idx], y.iloc[val_idx]
        
        model = classifier.fit(x_train, y_train)
        val_preds = model.predict(x_val)
        
        mae += mean_absolute_error(y_val, val_preds) / PARAM.FOLD
        mse += mean_squared_error(y_val,val_preds) / PARAM.FOLD
        rmse += np.sqrt(mean_squared_error(y_val, val_preds)) / PARAM.FOLD
        r2score += r2_score(y_val,val_preds)/PARAM.FOLD
        
        print('Fold','{',fold_idx+1,'} ','\n\n')
        print('MAE Score: ', mean_absolute_error(y_val, val_preds))
        print('MSE Score: ', mean_squared_error(y_val,val_preds))
        print('RMSE Score: ', np.sqrt(mean_squared_error(y_val, val_preds)))
        print('R2 Score: ', r2_score(y_val,val_preds),'\n\n')
        
    mae_score.append(round(mae,2))
    mse_score.append(round(mse,2))
    rmse_score.append(round(rmse,2))
    R2_score.append(round(r2score,2))
    print('---'*20,'\n')

Classifier: XGBRegressor 


Fold { 1 }  


MAE Score:  2351.7978405898875
MSE Score:  8155625.990826296
RMSE Score:  2855.8056640510913
R2 Score:  0.9687657682665701 


Fold { 2 }  


MAE Score:  2133.407654494382
MSE Score:  8526821.493984265
RMSE Score:  2920.072172735507
R2 Score:  0.9738206370914442 


Fold { 3 }  


MAE Score:  2056.7740080758426
MSE Score:  6287667.866665101
RMSE Score:  2507.5222564645564
R2 Score:  0.9741115953795728 


Fold { 4 }  


MAE Score:  2093.392819522472
MSE Score:  6314967.332763586
RMSE Score:  2512.959874881329
R2 Score:  0.9807405855385888 


Fold { 5 }  


MAE Score:  2153.180016678371
MSE Score:  6657908.637094005
RMSE Score:  2580.292354965616
R2 Score:  0.9775929633004001 


Fold { 6 }  


MAE Score:  2102.8845022823034
MSE Score:  6654860.362172374
RMSE Score:  2579.7016033201153
R2 Score:  0.9773778710502821 


Fold { 7 }  


MAE Score:  2164.418912394663
MSE Score:  7467270.192870451
RMSE Score:  2732.630636011836
R2 Score:  0.9790459623858546 


Fold { 8 }  


MAE Score:  2108.505948153409
MSE Score:  7006145.203415263
RMSE Score:  2646.912390581763
R2 Score:  0.9772202660727837 


Fold { 9 }  


MAE Score:  1972.9376775568182
MSE Score:  6121307.638388547
RMSE Score:  2474.1276519994976
R2 Score:  0.9719660366785701 


Fold { 10 }  


MAE Score:  1938.199618252841
MSE Score:  5428177.976556778
RMSE Score:  2329.8450541949733
R2 Score:  0.977818259405261 


------------------------------------------------------------ 

Classifier: LGBMRegressor 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000394 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 798, number of used features: 5
[LightGBM] [Info] Start training from score 59545.213033
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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Fold { 1 }  


MAE Score:  2311.5209559868326
MSE Score:  7649408.510867342
RMSE Score:  2765.756408447306
R2 Score:  0.9707044685078926 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000468 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 798, number of used features: 5
[LightGBM] [Info] Start training from score 59056.115288
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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Fold { 2 }  


MAE Score:  2138.205559388096
MSE Score:  7581808.1228597015
RMSE Score:  2753.508329905632
R2 Score:  0.9767220521162059 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000277 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 798, number of used features: 5
[LightGBM] [Info] Start training from score 59473.095238
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
Fold { 3 }  


MAE Score:  1910.8402607667513
MSE Score:  5103154.333956708
RMSE Score:  2259.0162314504755
R2 Score:  0.9789886286872165 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000419 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 798, number of used features: 5
[LightGBM] [Info] Start training from score 59270.476190
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
Fold { 4 }  


MAE Score:  2224.6962349514133
MSE Score:  6647105.754995954
RMSE Score:  2578.198160536919
R2 Score:  0.979727628353657 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000524 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 798, number of used features: 5
[LightGBM] [Info] Start training from score 59351.817043
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
Fold { 5 }  


MAE Score:  2147.0986509109152
MSE Score:  6868750.095559114
RMSE Score:  2620.830039426272
R2 Score:  0.9768833812747016 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000223 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 798, number of used features: 5
[LightGBM] [Info] Start training from score 59186.052632
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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Fold { 6 }  


MAE Score:  1763.5866121878657
MSE Score:  4509558.618214871
RMSE Score:  2123.57213633417
R2 Score:  0.9846704797673219 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000343 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 798, number of used features: 5
[LightGBM] [Info] Start training from score 59343.583960
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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Fold { 7 }  


MAE Score:  2300.478760199197
MSE Score:  10065439.836642873
RMSE Score:  3172.607734442264
R2 Score:  0.9717551930635502 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000662 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 799, number of used features: 5
[LightGBM] [Info] Start training from score 59281.314143
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
Fold { 8 }  


MAE Score:  1962.686883870501
MSE Score:  6061322.487507732
RMSE Score:  2461.9753222783797
R2 Score:  0.980292256368713 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000276 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 799, number of used features: 5
[LightGBM] [Info] Start training from score 58980.625782
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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Fold { 9 }  


MAE Score:  2055.2170674082327
MSE Score:  6390092.747358832
RMSE Score:  2527.863277030392
R2 Score:  0.9707350722619208 


[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000418 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 787
[LightGBM] [Info] Number of data points in the train set: 799, number of used features: 5
[LightGBM] [Info] Start training from score 59682.966208
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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Fold { 10 }  


MAE Score:  1854.5934942008541
MSE Score:  4980957.304964811
RMSE Score:  2231.8058394414174
R2 Score:  0.9796457847680441 


------------------------------------------------------------ 

Classifier: CatBoostRegressor 


Fold { 1 }  


MAE Score:  2262.0966580819036
MSE Score:  7266437.489466399
RMSE Score:  2695.633040579967
R2 Score:  0.9721711622531772 


Fold { 2 }  


MAE Score:  2008.9580105083803
MSE Score:  7272972.175240019
RMSE Score:  2696.844855611835
R2 Score:  0.9776702516718841 


Fold { 3 }  


MAE Score:  1970.407915866328
MSE Score:  5142451.972313902
RMSE Score:  2267.6975045878366
R2 Score:  0.9788268273351107 


Fold { 4 }  


MAE Score:  2123.8003975808074
MSE Score:  6312103.669118533
RMSE Score:  2512.390031248837
R2 Score:  0.9807493191522579 


Fold { 5 }  


MAE Score:  1963.7821250321158
MSE Score:  5793785.6525047105
RMSE Score:  2407.0283863105374
R2 Score:  0.9805011491112994 


Fold { 6 }  


MAE Score:  1973.3100519054285
MSE Score:  5561393.084904211
RMSE Score:  2358.2606058076385
R2 Score:  0.9810949374352156 


Fold { 7 }  


MAE Score:  2043.9624066813112
MSE Score:  6741990.893486401
RMSE Score:  2596.5344005975353
R2 Score:  0.9810811813249743 


Fold { 8 }  


MAE Score:  2042.472590524421
MSE Score:  7106574.525257251
RMSE Score:  2665.8159211125685
R2 Score:  0.9768937308435486 


Fold { 9 }  


MAE Score:  1914.9489307690928
MSE Score:  5632100.339979937
RMSE Score:  2373.204656151664
R2 Score:  0.9742064761843638 


Fold { 10 }  


MAE Score:  1840.8457052849596
MSE Score:  4655308.157408492
RMSE Score:  2157.616313761205
R2 Score:  0.9809765194910375 


------------------------------------------------------------ 

Classifier: RandomForestRegressor 


Fold { 1 }  


MAE Score:  2266.619101123595
MSE Score:  7237499.20213483
RMSE Score:  2690.260062175185
R2 Score:  0.9722819894506848 


Fold { 2 }  


MAE Score:  2026.6943820224722
MSE Score:  7119549.913932586
RMSE Score:  2668.2484730497995
R2 Score:  0.9781412943763493 


Fold { 3 }  


MAE Score:  1823.3595505617977
MSE Score:  4796708.57280899
RMSE Score:  2190.1389391563703
R2 Score:  0.9802503670657442 


Fold { 4 }  


MAE Score:  2139.7685393258425
MSE Score:  6387892.4170786515
RMSE Score:  2527.4280241143665
R2 Score:  0.9805181783036107 


Fold { 5 }  


MAE Score:  2145.51011235955
MSE Score:  6420844.163146066
RMSE Score:  2533.938468697704
R2 Score:  0.9783907982749338 


Fold { 6 }  


MAE Score:  1826.5067415730339
MSE Score:  4771231.533370786
RMSE Score:  2184.3148887856773
R2 Score:  0.9837809647201011 


Fold { 7 }  


MAE Score:  1917.131460674157
MSE Score:  5842939.695393259
RMSE Score:  2417.2173455014877
R2 Score:  0.9836040246312033 


Fold { 8 }  


MAE Score:  1918.584090909091
MSE Score:  5636907.400454544
RMSE Score:  2374.2172184647607
R2 Score:  0.9816721967606213 


Fold { 9 }  


MAE Score:  1987.2897727272727
MSE Score:  5933875.519886363
RMSE Score:  2435.9547450407126
R2 Score:  0.9728244260041442 


Fold { 10 }  


MAE Score:  1732.690909090909
MSE Score:  4386826.4179545455
RMSE Score:  2094.47521301985
R2 Score:  0.9820736449583144 


------------------------------------------------------------ 

Classifier: DecisionTreeRegressor 


Fold { 1 }  


MAE Score:  2849.438202247191
MSE Score:  12274035.95505618
RMSE Score:  3503.4320251799063
R2 Score:  0.9529931750480096 


Fold { 2 }  


MAE Score:  2444.044943820225
MSE Score:  11652795.505617978
RMSE Score:  3413.619121345845
R2 Score:  0.9642231559959376 


Fold { 3 }  


MAE Score:  2474.1573033707864
MSE Score:  8887676.404494382
RMSE Score:  2981.2206232505473
R2 Score:  0.9634065017786938 


Fold { 4 }  


MAE Score:  2673.14606741573
MSE Score:  10171331.460674157
RMSE Score:  3189.2524924618556
R2 Score:  0.968979429678255 


Fold { 5 }  


MAE Score:  2458.0898876404494
MSE Score:  9285412.359550562
RMSE Score:  3047.1974598884403
R2 Score:  0.9687501606206812 


Fold { 6 }  


MAE Score:  2253.483146067416
MSE Score:  7892948.314606742
RMSE Score:  2809.4391459162703
R2 Score:  0.9731691899079598 


Fold { 7 }  


MAE Score:  2963.932584269663
MSE Score:  12907428.089887641
RMSE Score:  3592.690926017383
R2 Score:  0.9637802400727895 


Fold { 8 }  


MAE Score:  2372.7272727272725
MSE Score:  9112275.0
RMSE Score:  3018.65450159504
R2 Score:  0.9703724096568196 


Fold { 9 }  


MAE Score:  2230.0
MSE Score:  8370002.2727272725
RMSE Score:  2893.0956210825925
R2 Score:  0.9616676124489485 


Fold { 10 }  


MAE Score:  2052.840909090909
MSE Score:  7464053.409090909
RMSE Score:  2732.0419852357522
R2 Score:  0.9694988452440623 


------------------------------------------------------------ 

Classifier: LinearRegression 


Fold { 1 }  


MAE Score:  12832.229342291097
MSE Score:  284152610.0125408
RMSE Score:  16856.82680733657
R2 Score:  -0.08824123111749183 


Fold { 2 }  


MAE Score:  12858.037464659667
MSE Score:  279654184.41571724
RMSE Score:  16722.86412118801
R2 Score:  0.14139537365941024 


Fold { 3 }  


MAE Score:  10648.126941375698
MSE Score:  196297339.25260094
RMSE Score:  14010.615234621246
R2 Score:  0.1917790423653648 


Fold { 4 }  


MAE Score:  13008.241547675423
MSE Score:  276453773.7965929
RMSE Score:  16626.899103458614
R2 Score:  0.15687009474366442 


Fold { 5 }  


MAE Score:  13415.022450210268
MSE Score:  294475895.57638544
RMSE Score:  17160.299985034802
R2 Score:  0.008948220982560096 


Fold { 6 }  


MAE Score:  12248.48486531663
MSE Score:  247939293.48328057
RMSE Score:  15746.088196224502
R2 Score:  0.1571701938686807 


Fold { 7 }  


MAE Score:  13611.536559211492
MSE Score:  332877119.9663761
RMSE Score:  18244.920388052564
R2 Score:  0.06590768614165243 


Fold { 8 }  


MAE Score:  11797.263488824992
MSE Score:  236268972.62845984
RMSE Score:  15371.043316198802
R2 Score:  0.23179663345979962 


Fold { 9 }  


MAE Score:  10204.39714537485
MSE Score:  169729222.76416266
RMSE Score:  13028.016839264626
R2 Score:  0.22268523547070784 


Fold { 10 }  


MAE Score:  10236.026727509974
MSE Score:  179123377.22634733
RMSE Score:  13383.698189452247
R2 Score:  0.2680291056689439 


------------------------------------------------------------

Model Comparison¶

Compare R2 Score of 5 regression models below:¶

In [70]:
fig = px.bar(x = classifiers_name,
             y = R2_score,
             text = R2_score,
             template = "simple_white",
             color = classifiers_name,
             color_discrete_sequence = px.colors.qualitative.Antique)

fig.update_layout(template = 'simple_white', title = 'R2 Score Comparison')

fig.update_layout(
    xaxis_title="Models",
    yaxis_title="R2_Score",
    font = dict(size=17, family = 'Franklin Gothic'))


fig.data[2].marker.line.width = 3
fig.data[2].marker.line.color='black'
    
fig.show()

Observations:¶

  • The R2 score is a measure of how well the variations in the dependent variable can be explained by the independent variables in a regression model. A higher R2 score indicates a better fit.

  • XGBRegressor, LGBMRegressor, CatBoostRegressor, and RandomForestRegressor all have the same R2 scores of 0.98, which is very close to 1, indicating an excellent fit.

  • DecisionTreeRegressor has a slightly lower R2 score of 0.96, which is still considered very good.

  • LinearRegression has a significantly lower R2 score of 0.02, which indicates a poor fit.

Our 'CatBoostRegressor' model got the highest R2_Score.¶¶

And RMSE Score Comparison:¶

In [71]:
fig = px.line(x = classifiers_name,
             y = rmse_score,
             text = rmse_score,
             template = "simple_white",)

fig.update_layout(template = 'simple_white', title = 'RMSE Score Comparison')

fig.update_layout(
    xaxis_title="Models",
    yaxis_title="RMSE_Score",
    font = dict(size=17, family = 'Franklin Gothic'))

fig.show()

Observations:¶

  • RMSE is a measure of the average magnitude of the errors between the predicted values from the model and the actual values. A lower RMSE indicates better performance.

  • The RMSE scores for XGBRegressor, LGBMRegressor, CatBoostRegressor, and RandomForestRegressor are relatively low and quite close to each other, ranging from 2452.75 to 2656.17.

  • DecisionTreeRegressor has a higher RMSE of 3247.01, indicating that the average error of the predictions is greater.

  • LinearRegression has an extremely high RMSE of 16762.13, which indicates very poor predictive performance.

¶

Which Model is Best?¶

Based on the R2 score, all models except LinearRegression perform excellently, with no clear winner. However, when considering the RMSE, which gives us an idea about the error magnitude, XGBRegressor has the lowest RMSE, followed closely by LGBMRegressor, CatBoostRegressor, and RandomForestRegressor.¶

Considering both metrics together, XGBRegressor might be the best model due to its high R2 score and the lowest RMSE. However, the choice of the best model can also depend on other factors such as the complexity of the model, the time it takes to train, and the nature of the data. Additionally, the very high performance of multiple models could indicate that the problem is relatively straightforward or that the data might not be challenging enough to differentiate the models' performance. It's also worth considering whether the models are overfitting given the extremely high R2 scores.¶

¶

¶

Prediction¶

As we analyse in above model comparison, XGB regressor might be the best model due to its high R2 score and the lowest RMSE.So let us Predict new values with the help of XGB regressor model¶

¶

In [72]:
import xgboost as xgb


# Calculate the mean and standard deviation for each feature
mean_area = Store['Store_Area'].mean()
std_area = Store['Store_Area'].std()
mean_items = Store['Items_Available'].mean()
std_items = Store['Items_Available'].std()
mean_customers = Store['Daily_Customer_Count'].mean()
std_customers = Store['Daily_Customer_Count'].std()

# Generate synthetic data for 10 new stores
np.random.seed(42)  # For reproducibility
synthetic_store_area = np.random.normal(mean_area, std_area, 10).astype(int)
synthetic_items_available = np.random.normal(mean_items, std_items, 10).astype(int)
synthetic_daily_customer_count = np.random.normal(mean_customers, std_customers, 10).astype(int)

# Ensure all synthetic values are positive (assuming all these features are positive)
synthetic_store_area = np.abs(synthetic_store_area)
synthetic_items_available = np.abs(synthetic_items_available)
synthetic_daily_customer_count = np.abs(synthetic_daily_customer_count)

# Create a DataFrame with the synthetic data
synthetic_data = pd.DataFrame({
    'Store_Area': synthetic_store_area,
    'Items_Available': synthetic_items_available,
    'Daily_Customer_Count': synthetic_daily_customer_count
})

# Train the XGBRegressor model on the entire dataset
X = Store[['Store_Area', 'Items_Available', 'Daily_Customer_Count']]
y = Store['Store_Sales']
xgb_model = xgb.XGBRegressor(objective='reg:squarederror')
xgb_model.fit(X, y)

# Predict the Store_Sales for the synthetic data points
predicted_sales = xgb_model.predict(synthetic_data)

# Output the synthetic data and corresponding predicted sales
synthetic_data['Predicted_Store_Sales'] = predicted_sales
print(synthetic_data)

   Store_Area  Items_Available  Daily_Customer_Count  Predicted_Store_Sales
0        1605             1645                  1170           66251.398438
1        1450             1644                   726           65918.453125
2        1642             1851                   803           72965.281250
3        1855             1221                   411           76570.921875
4        1427             1276                   642           65781.867188
5        1427             1616                   814           55044.460938
6        1869             1484                   483           82657.656250
7        1671             1872                   884           46013.390625
8        1369             1515                   627           57204.605469
9        1616             1368                   708           66086.148438
The Above is 10 predicted Store Sales values for the Dataset Stores.csv¶

Observations:¶

- Theres a significant range in the predicted sales, indicating that the model can differentiate well between various store scenarios.

- Higher daily customer counts seem to correspond to higher predicted sales, which suggests that customer count is a strong predictor in the model.

- The relationship between store area, items available, and sales is not clearly linear, which is expected given the complexity usually captured by gradient boosting models like XGBRegressor.

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